Joseph P. Romano

Testing Statistical Hypotheses, 4th Edition updates and expands upon the classic graduate text, now a two-volume work. The first volume covers finite-sample theory, while the second volume discusses large-sample theory. A definitive resource for graduate students and researchers alike, this work grows to include new topics of current relevance. New additions include an expanded treatment of multiple hypothesis testing, a new section on extensions of the Central Limit Theorem, coverage of high-dimensional testing, expanded discussions of permutation and randomization tests, coverage of testing moment inequalities, and many new problems throughout the text.

Testing Statistical Hypotheses, 4th Edition updates and expands upon the classic graduate text, now a two-volume work. The first volume covers finite-sample theory, while the second volume discusses large-sample theory. A definitive resource for graduate students and researchers alike, this work grows to include new topics of current relevance. New additions include an expanded treatment of multiple hypothesis testing, a new section on extensions of the Central Limit Theorem, coverage of high-dimensional testing, expanded discussions of permutation and randomization tests, coverage of testing moment inequalities, and many new problems throughout the text.

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. The primary goal of this book is to lay some of the foundation for subsampling methodology and related methods.

The Third Edition of Testing Statistical Hypotheses brings it into consonance with the Second Edition of its companion volume on point estimation (Lehmann and Casella, 1998) to which we shall refer as TPE2. We won’t here comment on the long history of the book which is recounted in Lehmann (1997) but shall use this Preface to indicate the principal changes from the 2nd Edition. The present volume is divided into two parts. Part I (Chapters 1–10) treats small-sample theory, while Part II (Chapters 11–15) treats large-sample theory. The preface to the 2nd Edition stated that “the most important omission is an adequate treatment of optimality paralleling that given for estimation in TPE.” We shall here remedy this failure by treating the di?cult topic of asymptotic optimality (in Chapter 13) together with the large-sample tools needed for this purpose (in Chapters 11 and 12). Having developed these tools, we use them in Chapter 14 to give a much fuller treatment of tests of goodness of ?tthan was possible in the 2nd Edition, and in Chapter 15 to provide an introduction to the bootstrap and related techniques. Various large-sample considerations that in the Second Edition were discussed in earlier chapters now have been moved to Chapter 11.

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. The primary goal of this book is to lay some of the foundation for subsampling methodology and related methods.